What is the Least Common Multiple of 7305 and 7314?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 7305 and 7314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7305 and 7314, than apply into the LCM equation.

GCF(7305,7314) = 3
LCM(7305,7314) = ( 7305 × 7314) / 3
LCM(7305,7314) = 53428770 / 3
LCM(7305,7314) = 17809590

Least Common Multiple (LCM) of 7305 and 7314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7305 and 7314. First we will calculate the prime factors of 7305 and 7314.

Prime Factorization of 7305

Prime Factorization of 7314

Now multiplying the highest exponent prime factors to calculate the LCM of 7305 and 7314.

LCM(7305,7314) = 3¹ × 5¹ × 487¹ × 2¹ × 23¹ × 53¹
LCM(7305,7314) = 17809590